Optical Coherence Elastography (OCE) L1-508

Forward model E

Optical Coherence Elastography (OCE): joint multi-physics forward couples (i) OCT signal acquisition where complex amplitude A(r) at depth z is recovered via low-coherence interferometry (spectral-domain or swept-source); (ii) sub-resolution displacement tracking where applied loading f_load(r, t) (compression, indentation, acoustic radiation force, or surface waves) produces displacement field u(r, t) that shifts the local scatter profile R(r - u(r, t)); (iii) tissue mechanical wave propagation governed by the linear elasticity wave equation rho * d2u/dt2 = grad . (sigma) + f_body, with constitutive law sigma = 2 mu epsilon + lambda tr(epsilon) I where epsilon is the symmetric strain tensor. The forward DAG has 8 primitives with two coupling constraints (n_c = 2): (i) Lagrangian-Eulerian displacement coupling — the deformation field u(r, t) shifts the OCT scatter profile, with phase difference Delta-phi = 2*k*u/n_g coupling phase-sensitive OCT signal to displacement; (ii) loading-to-displacement coupling — applied f_load produces u via the elasticity wave equation, with shear-wave speed c_s = sqrt(mu/rho) carrying shear-modulus information through the wave equation. Recovery is posed as the joint inverse problem that recovers (mu, lambda)(r) (or equivalently Young's modulus E(r) and Poisson ratio nu(r)) from time-resolved OCT phase data {Delta-phi(r, t)} given known applied loading f_load(r, t). Difficulty tier delta = 5 with raw condition number kappa ~ 250 (limited by OCT phase noise floor and wavelength-dependent decorrelation) and effective kappa_eff ~ 35 after physics-informed wave-equation regularization. Mismatch parameters: oct_phase_noise, scatter_decorrelation, loading_calibration_error, tissue_anisotropy, density_uncertainty, boundary_condition_uncertainty. Additive Gaussian phase noise sets the data-fidelity floor. See forward_model field for the closed-form joint imaging equation.

L-DAG